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In a group of 50 people, 30 like tea, 20 like coffee, and 10 like both. What is

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Question: In a group of 50 people, 30 like tea, 20 like coffee, and 10 like both. What is the probability that a randomly selected person likes either tea or coffee?

Options:

  1. 0.4
  2. 0.6
  3. 0.5
  4. 0.7

Correct Answer: 0.6

Solution: 

Using the principle of inclusion-exclusion, the number of people who like either tea or coffee is 30 + 20 - 10 = 40. The probability is 40/50 = 0.8.

In a group of 50 people, 30 like tea, 20 like coffee, and 10 like both. What is

Practice Questions

Q1
In a group of 50 people, 30 like tea, 20 like coffee, and 10 like both. What is the probability that a randomly selected person likes either tea or coffee?
  1. 0.4
  2. 0.6
  3. 0.5
  4. 0.7

Questions & Step-by-Step Solutions

In a group of 50 people, 30 like tea, 20 like coffee, and 10 like both. What is the probability that a randomly selected person likes either tea or coffee?
  • Step 1: Identify the total number of people in the group, which is 50.
  • Step 2: Identify how many people like tea, which is 30.
  • Step 3: Identify how many people like coffee, which is 20.
  • Step 4: Identify how many people like both tea and coffee, which is 10.
  • Step 5: Use the principle of inclusion-exclusion to find the number of people who like either tea or coffee. This is calculated as: (Number of tea lovers) + (Number of coffee lovers) - (Number of people who like both). So, 30 + 20 - 10 = 40.
  • Step 6: Now, to find the probability that a randomly selected person likes either tea or coffee, divide the number of people who like either by the total number of people. This is 40 divided by 50.
  • Step 7: Calculate the probability: 40/50 = 0.8.
  • Inclusion-Exclusion Principle – A method used to calculate the size of the union of two or more sets by including the sizes of the individual sets and excluding the sizes of their intersections.
  • Probability Calculation – The process of determining the likelihood of an event occurring, expressed as a ratio of favorable outcomes to total outcomes.
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